Given a string S and a string T, count the number of distinct subsequences of T in S.
A subsequence of a string is a new string which is formed from the original string by deleting some (can be none) of the characters without disturbing the relative positions of the remaining characters. (ie, "ACE" is a subsequence of "ABCDE" while "AEC" is not).
Here is an example:
S = "rabbbit", T = "rabbit"
Return 3.
https://oj.leetcode.com/problems/distinct-subsequences/
思路：DP。dp[i][j]代表从s[0..i]中删除几个字符得到t[0..j]的不同删除方法数。
public class Solution { public int numDistinct(String S, String T) { int m = S.length(); int n = T.length(); int[][] dp = new int[m + 1][n + 1]; for (int i = 0; i <= m; i++) dp[i][0] = 1; for (int i = 1; i <= m; i++) { for (int j = 1; j <= n; j++) { if (S.charAt(i - 1) == T.charAt(j - 1)) dp[i][j] = dp[i - 1][j - 1] + dp[i - 1][j]; else dp[i][j] = dp[i - 1][j]; } } return dp[m][n]; } public static void main(String[] args) { String S = "rabbbit"; String T = "rabbit"; System.out.println(new Solution().numDistinct(S, T)); } }
参考：
http://www.programcreek.com/2013/01/leetcode-distinct-subsequences-total-java
http://www.cnblogs.com/TenosDoIt/p/3440022.html
[leetcode] Distinct Subsequences,布布扣,bubuko.com
[leetcode] Distinct Subsequences
原文：http://www.cnblogs.com/jdflyfly/p/3821464.html
